Global carbon dioxide emissions from energy sources reached approximately 37.4 billion tons in 2023, a 75.7% increase since 1990. Emerging economies, particularly China, are major contributors due to rapid economic growth and increased energy consumption. China's commitment to peaking carbon emissions by 2030 and achieving carbon neutrality by 2060, along with various international collaborations, underscores its efforts to address climate change. However, China's manufacturing sector, a core driver of its economy, faces significant challenges due to its large scale and energy-intensive industries. In 2020, it contributed 50% of global manufacturing emissions despite accounting for only 27.7% of China's GDP. This highlights the urgent need to balance economic growth with environmental protection and improve manufacturing carbon emission efficiency (MCEE). The role of enterprise size and transformation strategy in achieving MCEE is increasingly crucial. While large enterprises often have higher emissions, they may also benefit from economies of scale and technological innovation. This study investigates the complex relationship between enterprise size and MCEE in China's manufacturing sector, focusing on whether this relationship is linear or nonlinear and whether factors such as environmental regulation, R&D investment, and trade openness influence this relationship.

Measuring manufacturing carbon emission efficiency (MCEE) involves two main approaches: single-factor methods (e.g., carbon intensity) and total-factor methods. The total-factor approach, adopted in this study, provides a more comprehensive and accurate assessment by integrating inputs, desired outputs, and undesirable outputs. Methodology includes Stochastic Frontier Analysis (SFA) and Data Envelopment Analysis (DEA). While SFA faces challenges with undesirable outputs, DEA, particularly the non-radial directional distance function (NDDF) model, offers greater flexibility and applicability. Existing research exploring factors influencing MCEE considers internal factors (e.g., R&D investment) and external factors (e.g., environmental regulations, trade openness). However, studies on the impact of corporate size on MCEE are inconclusive, with some suggesting a positive effect due to economies of scale and technological innovation, and others suggesting a negative effect due to management complexity and resource misallocation. This study addresses these gaps by using a more comprehensive methodology and examining the interaction between firm size and several other key factors.

This study uses data from 29 sub-sectors of China's manufacturing industry from 2012 to 2021. It employs a non-radial directional distance function (NDDF) model to measure MCEE, considering labor input, capital input, energy input, industrial added value (expected output), and carbon dioxide emissions (undesired output). The NDDF model offers advantages over traditional DEA models by allowing for the specification of change directions and weights of variables. Carbon emissions are calculated using the energy consumption method, considering eight primary energy sources. Before regression analysis, unit root tests (LLC, IPS, Fisher ADF, Fisher PP) and a panel cointegration test (Kao) were conducted to ensure data stability and the presence of long-term equilibrium relationships. The study then employs three econometric models: Ordinary Least Squares (OLS), Fixed Effects (FE), and Generalized Method of Moments (GMM). The system GMM model accounts for potential endogeneity and autocorrelation. To analyze the nonlinear impact of corporate scale on MCEE, the study utilizes the moment quantile regression (MMQR) method, which accounts for both individual and conditional heterogeneity. Finally, a panel threshold model is used to investigate the threshold effects of environmental regulations, R&D investment, and trade openness on the relationship between corporate scale and MCEE. Corporate scale is proxied by the ratio of industrial value-added to the number of corporate units. Environmental regulation is measured by the ratio of operating costs for wastewater and gas emissions to main operating revenue. R&D investment is measured by the ratio of R&D funding to industrial added value. Trade openness is measured by the ratio of foreign and Hong Kong, Macau, and Taiwan investment to net fixed assets. Control variables include energy endowment, product structure, and market competition.

Unit root and cointegration tests confirmed the stationarity of the data and the existence of long-term equilibrium relationships among the variables. Benchmark regression analysis using the system GMM model showed a significantly positive relationship between corporate scale (CS) and MCEE. A 1% increase in CS led to a 2.5% increase in MCEE. Robustness tests using difference GMM, an alternative MCEE measurement (Super-SBM), a different corporate scale proxy, and a shortened sample period consistently supported this positive relationship. The MMQR model revealed a positive correlation between CS and MCEE across all quantile levels, with a stronger effect at lower quantiles of MCEE. The panel threshold model demonstrated threshold effects of environmental regulation (ER), R&D investment (RD), and trade openness (OPEN) on the CS-MCEE relationship. With ER below the threshold, a 1% increase in CS resulted in an 11.86% increase in MCEE; above the threshold, this increased to 22.68%. Similarly, the positive impact of CS on MCEE was stronger with higher RD. Conversely, greater OPEN weakened the positive effect of CS on MCEE. Specifically, the coefficient for CS in the model with OPEN as the threshold variable dropped from 0.2374 to 0.114 when OPEN surpassed the threshold value.

The findings confirm a significant positive relationship between corporate scale and MCEE in China's manufacturing sector, even after controlling for various factors and robustness checks. The nonlinear analysis indicates that the positive impact of scale is more pronounced at lower levels of MCEE, suggesting that scale expansion can be particularly beneficial for less efficient firms. The threshold effects highlight the importance of policy context. Stronger environmental regulations and higher R&D investment amplify the positive effect of scale, while greater trade openness may have a dampening effect. These findings have important implications for policymakers and businesses. They support policies that encourage scale expansion, but also emphasize the need for strategic management and resource allocation to realize the full environmental benefits of scale. The study's focus on China's specific context provides valuable insights for both emerging and developed economies.

This study provides strong evidence for the positive impact of corporate scale on MCEE in China's manufacturing sector. The findings highlight the importance of considering both the direct effects of scale and the moderating roles of environmental regulations, R&D investment, and trade openness. Future research could explore this relationship in other emerging economies, delve deeper into the mechanisms driving the nonlinear effects, and investigate other factors, such as resource misallocation and ownership structure, that may influence the relationship between firm size and CEE.

This study focuses solely on China's manufacturing sector, limiting the generalizability of findings to other countries and industries. The reliance on aggregated data may mask variations at the firm level. While the study incorporates several control variables, other unobserved factors could influence the relationship between firm size and MCEE. Further research should explore these potential confounding factors.